In this paper, we build a novel statistical framework in a multiple-multivariate regression set-up, which addresses the above mentioned challenges incorporating the aforementioned dependence structures within and between the responses and covariates. Specifically, we leverage the hierarchical model specification to incorporate the sequential nature of the spherical layer-based imaging phenotypes as well as the correlation between the genomic markers. We propose a Bayesian variable selection approach that allows us to incorporate prior structural information in a natural and principled manner within a decision-theoretic framework, and deals with the issue of high-dimensionality. Specifically, we use continuous structured spike-and-slab priors [1]}, [2]}, [3]} within the regression model for a specific layer to (i) blend prior information about the correlation between the genomic markers, and (ii) borrow information about the selected genomic markers from the estimation at one spherical layer and propagate the information through the prior of the model to the subsequent spherical layer(s). As opposed to existing approaches that incorporate apriori structural information [4]}, [5]}, our prior formulation incorporates structural information not only for the dependence between the predictors, but also for the dependence between the multivariate response and across the spherical layers.
